Modified flow rate analysis

ABSTRACT

Methods, systems, devices, and products for estimating a parameter of interest of an earth formation. The method may include using a correction factor to conduct a flow rate analysis on fluid sampled from the formation via a probe contacting a wall of the borehole, wherein the correction factor compensates for total compressibility; determining at least one of: i) the product of formation porosity and total compressibility; ii) system compressibility; and iii) initial formation pressure; or determining a mobility of the formation using a slope of a linear relationship of a time-dependent pressure of the fluid with respect to a formation flow rate. The parameter of interest may be i) formation mobility or ii) formation permeability. The correction factor may be determined using formation compressibility. The correction factor may be determined using at least one of: i) gas saturation; ii) oil saturation; and iii) water saturation.

FIELD OF THE DISCLOSURE

This disclosure generally relates to borehole tools, and in particularto methods and apparatuses for conducting downhole measurements.

BACKGROUND OF THE DISCLOSURE

Historically, flow rate analysis has been used to determine parametersof interest such as formation permeability and fluid mobility. Toolsconfigured to extract formation fluids from the wall of a borehole arewell known. Generally, such tools include a fluid entry port which maybe part of a probe associated with a pad engageable to the wall of theborehole. One or more packers may also be used. Fluids (liquids, gases,mixtures, and so on) from the formation may be drawn in to the port andto a chamber while the pressure and volume are measured.

Conventionally, a draw down test method may be used for determiningpermeability. With the probe engaged against the borehole wall, ameasured volume of fluid is withdrawn from the formation. The method mayinclude reducing pressure in a flow line that is in fluid communicationwith a borehole wall. A piston may be used to increase the flow linevolume, thereby decreasing the flow line pressure. The rate of pressuredecrease is such that formation fluid entering the flow line combineswith fluid leaving the flow line to create a substantially linearpressure decrease. Generally, the fluid pressure in the formation at thewall of the wellbore is monitored until equilibrium pressure is reached.Conversely, in the buildup method, fluid is withdrawn from the reservoirusing a probe and the flow of fluid is terminated. The subsequentbuildup in pressure is measured.

In some techniques, a “best straight line fit” is used to define astraight-line reference for a predetermined acceptable deviationdetermination. The acceptable deviation may be 2σ from the straightline. Once the straight-line reference is determined, the volumeincrease is maintained at a steady rate. At a first time, the pressureexceeds the 2σ limit and it is assumed that the flow line pressure beingbelow the formation pressure causes the deviation. Draw down isdiscontinued and the pressure is allowed to stabilize. Additional drawdown cycles may be repeated. Various improvements to the tool haveoccurred over time, allowing faster, safer or more accuratedetermination of pressure and/or volume.

In other methods, draw down may continue at an established rate untilthe formation fluid entering the tool stabilizes the tool pressure. Thenthe pressure is allowed to rise and stabilize by stopping the draw down.Other methods may include incrementally decreasing the pressure withinthe test volume at a variable rate to allow periodic measurements ofpressure as the test volume pressure decreases. Adjustments to the rateof decrease may be carried out before the pressure stabilizes.

SUMMARY OF THE DISCLOSURE

In aspects, the present disclosure is related to methods and apparatusesfor estimating at least downhole parameter relating to an earthformation intersected by a borehole.

One general method embodiment according to the present disclosure mayinclude using a correction factor to conduct a flow rate analysis onfluid sampled from the formation via a probe contacting a wall of theborehole, wherein the correction factor compensates for totalcompressibility. The method may include determining at least one of: i)the product of formation porosity and total compressibility; ii) systemcompressibility; and iii) initial formation pressure. The method mayinclude determining a mobility of the formation using a slope of alinear relationship of a time-dependent pressure of the fluid withrespect to a formation flow rate. The method may include applying thecorrection factor to pressure measurements of the sampled fluid toderive the time-dependent pressure. The method may include sampling thefluid from the formation; taking fluid pressure measurements over time;determining a volume of the sampled fluid as a function of time; anddetermining a corresponding draw rate of the formation fluid as afunction of time.

The parameter of interest may be at least one of: i) formation mobility;and ii) formation permeability. The correction factor may be determinedusing at least one of: i) a complementary error function; and ii)numerical inversion of laplace transform. The correction factor may bedetermined using estimated formation porosity and at least one of: i)predicted formation permeability; and ii) predicted formation mobility.The correction factor may be determined using a geometric factor. Thecorrection factor may be determined using both draw-down and build-upmeasurements. The correction factor may be determined usingsuperposition. The correction factor may be determined using formationcompressibility. The correction factor may be determined using at leastone of: i) gas saturation; ii) oil saturation; and iii) watersaturation.

Another general method embodiment includes modeling the formation usingan adjusted time-dependent pressure of a fluid sampled from theformation through a probe extending to the formation through a wall ofthe borehole, wherein the adjusted time-dependent pressure is determinedby applying a correction factor compensating for total compressibilityto time-dependent pressure measurements of the fluid.

Apparatus embodiments may include a tool body; a fluid sampling unitassociated with the tool body configured to sample fluid from theformation while in the borehole, the fluid sampling unit including aprobe configured to contact a wall of the borehole; and a processorconfigured to use a correction factor to conduct a flow rate analysis onfluid sampled from the formation by the fluid sampling unit, wherein thecorrection factor compensates for total compressibility.

The processor may be configured to carry out the methods describedabove. The processor may be configured to determine at least one of: i)the product of formation porosity and total compressibility; ii) systemcompressibility; and iii) initial formation pressure. The processor maybe configured to determine a mobility of the formation using a slope ofa linear relationship of a time-dependent pressure of the fluid withrespect to a formation flow rate. The processor may be configured toapply the correction factor to pressure measurements of the sampledfluid to derive the time-dependent pressure.

Further embodiments may include a non-transitory computer-readablemedium product having instructions thereon that, when executed, cause atleast one processor to perform a method as described above. The productmay have instructions thereon that cause the at least one processor touse a correction factor to conduct a flow rate analysis on fluid sampledfrom the formation via a probe contacting a wall of the borehole,wherein the correction factor compensates for total compressibility. Thenon-transitory computer-readable medium product may include at least oneof: (i) a ROM, (ii) an EPROM, (iii) an EEPROM, (iv) a flash memory, or(v) an optical disk.

Examples of some features of the disclosure may be summarized ratherbroadly herein in order that the detailed description thereof thatfollows may be better understood and in order that the contributionsthey represent to the art may be appreciated.

BRIEF DESCRIPTION OF THE DRAWINGS

For a detailed understanding of the present disclosure, reference shouldbe made to the following detailed description of the embodiments, takenin conjunction with the accompanying drawings, in which like elementshave been given like numerals, wherein:

FIG. 1 schematically illustrates a drilling system in accordance withembodiments of the present disclosure;

FIG. 2 is a section of drill string in accordance with embodiments ofthe present disclosure;

FIG. 3 illustrates a formation sampling tool in accordance withembodiments of the present disclosure;

FIG. 4 illustrates a wireline tool in accordance with embodiments of thepresent disclosure in communication with the formation;

FIG. 5 shows a downhole formation multi-tester instrument in accordancewith embodiments of the present disclosure;

FIGS. 6A and 6B show charts of dimensionless adjustment pressure withrespect to dimensionless time;

FIG. 7A compares an FRA plot created using the prior art method againsta corrected FRA plot;

FIG. 7B shows adjustment pressure with respect to time;

FIG. 8 shows a flow chart for estimating a parameter of interest of anearth formation intersected by a borehole in accordance with embodimentsof the present disclosure;

FIG. 9 shows a flow chart for using a correction factor to conduct aflow rate analysis on the fluid sampled from the formation in accordancewith embodiments of the present disclosure.

DETAILED DESCRIPTION

In aspects, this disclosure relates to estimating a parameter ofinterest of an earth formation intersected by a borehole. The at leastone parameter of interest may include, but is not limited to, one ormore of: (i) mobility, (ii) permeability, (iii) viscosity. The methodmay include using a correction factor to conduct a flow rate analysis onfluid sampled from the formation via a probe contacting a wall of theborehole. The correction factor may compensate for totalcompressibility.

Various analysis techniques have been used to analyze the informationgathered using a formation testing tool. One drawdown mobilitycalculation incorporates the pressure drawdown corresponding to thepiston drawdown rate in Darcy's equation to calculate near wellboremobility. Flow geometry may be modeled as a hemispherical flow about theprobe of the tool. Mobility estimates of low permeability formations areproblematic using these techniques due to tool storage effects.

New techniques were developed to calculate mobility using a formationrate analysis (FRA) methods accounting for storage effects. For example,some FRA methods account for storage effects using an estimated fluidcompressibility within the tool volume during drawdown. For example,formation flow rate may be calculated from the piston drawdown rateusing Darcy's equation and the material balance in the tool,

q _(ac) =q _(f) −q _(dd)

wherein q_(ac) represents accumulation, q_(f) represents formation flowand q_(dd) represents piston drawdown. A small density variation isimplicitly assumed. Time dependent pressure, p(t), may be calculated. Aplot of p(t) with respect to formation rate should approach a straightline with negative slope and intercept p* at the p(t) axis. Formationmobility and/or permeability may be calculated from the slope. The FRAplot should yield identical slopes for both buildup and drawdown in thecase of constant compressibility.

However, in the case of very low mobility (VLM) formations, this FRAmethodology does not produce reliable results. Specifically, theresulting FRA curve demonstrates significant deviation from a straightline, resulting in erroneously high mobility estimates. In VLMformations, accuracy may be significantly improved by accounting foreffects outside of the tool volume in order to estimate totalcompressibility of the fluid system. For example, FRA may be carried outby modeling the system including interactions between the fluid outsideof the tool and the rock of the formation.

Aspects of the present disclosure allow for estimating a parameter ofinterest of an earth formation intersected by a borehole. The method mayinclude using a correction factor to conduct a flow rate analysis onfluid sampled from the formation via a probe contacting a wall of theborehole, wherein the correction factor compensates for totalcompressibility. Total compressibility may be defined as compressibilityof the fluid system modeled by taking into account compressibilities andsaturations of predominant fluids in the tool-formation system alongwith the compressibility of the rock matrix corresponding to the portionof the formation containing such fluids and interacting with thesampling tool. For example, total compressibility may be defined ascompressibility of the fluid system modeled as a function of rockcompressibility, oil compressibility, water compressibility, oilcompressibility, gas compressibility, oil saturation, water saturation,gas saturation, and so on, or combinations of the same.

Some aspects include using information obtained from sensors associatedwith FRA instruments (FRA information). For example, such FRAinformation may include volume and pressure measurements with respect totime. Each of the embodiments herein may be used in a variety ofsettings in both drilling and non-drilling environments. In someimplementations, the disclosed embodiments may be used as part of adrilling system. An example drilling system for use in conjunction withLWD is illustrated herein.

FIG. 1 schematically illustrates a drilling system 100 having a downholetool 112 configured to acquire information for downhole fluid analysisin a borehole 104 intersecting a formation 119 using a test apparatus116. The system 100 includes a drilling rig 102 having a drill string106 extending therefrom. The drill string 106 has attached thereto abottom hole assembly (BHA) 108 including a drill bit for drillingborehole 104. Drill string may include jointed tubing, coiled tubing, orother small diameter work string such as snubbing pipe. Otherembodiments may include a slickline, an e-line, a wireline, etc. Thus,depending on the configuration, the tool may be used during drillingand/or after the wellbore (borehole) has been formed. The drillstring orother carrier may include embedded conductors for power and/or data forproviding signal and/or power communication between the surface anddownhole equipment.

The drilling rig 102 is shown positioned on a drilling ship 122 with ariser 124 extending from the drilling ship 122 to the sea floor 120.While a subsea system is shown, the teachings of the present disclosuremay also be utilized in land applications. Any drilling rigconfiguration may be adapted to implement the present disclosure. Ifapplicable, the drill string 106 may have a downhole drill motor (e.g.,mud motor) 110. Incorporated in the drill string 106 above the BHA 108is a typical testing unit, which can have one or more sensors 114 tosense downhole characteristics of the borehole, the BHA, the formationand/or the reservoir, with such sensors being well known in the art.Sensors 114 may detect one or more parameters of a formation. Parametersof a formation may include information relating to a geologicalparameter, a geophysical parameter, a petrophysical parameter, and/or alithological parameter. Thus, the sensors 114 may include sensors forestimating formation resistivity, dielectric constant, the presence orabsence of hydrocarbons, acoustic porosity, bed boundary, formationdensity, nuclear porosity and certain rock characteristics,permeability, capillary pressure, and relative permeability. Sensors 114may detect one or more parameters of the wellbore, including parametersrelating to downhole fluids. Non-limiting examples of downhole fluidsinclude drilling fluids, return fluids, formation fluids, productionfluids containing one or more hydrocarbons, oils and solvents used inconjunction with downhole tools, water, brine, engineered fluids, andcombinations thereof. A useful application of the sensor(s) 114 is todetermine direction, azimuth and orientation of the drill string 106,e.g., wherein the sensor may be an accelerometer or similar sensor. TheBHA also contains a formation test apparatus 116 according to thepresent disclosure, which will be described in greater detail below.

In order to operate the downhole tool 112 and/or provide acommunications interface with at least one processor at the surface, thedownhole tool 112 may include a downhole processor 117. In oneembodiment, electronics (not shown) associated with the sensors may beconfigured to record information related to the parameters to beestimated. In some embodiments, the parameter of interest may beestimated using the recorded information.

In other embodiments, such electronics may be located elsewhere (e.g.,at the surface). To perform estimation of a parameter during a singletrip, the tool may use a “high bandwidth” transmission to transmit theinformation acquired by sensors to the surface for analysis. Forinstance, a communication line for transmitting the acquired informationmay be an optical fiber, a metal conductor, or any other suitable signalconducting medium. It should be appreciated that the use of a “highbandwidth” communication line may allow surface personnel to monitor andcontrol the treatment activity in “real time.”

In some embodiments, processors may include electromechanical and/orelectrical circuitry configured to control one or more components of thetool 112. In other embodiments, processors may use algorithms andprogramming to receive information and control operation of the tool112, including the test apparatus 116. Therefore, processors may includean information processor that is in data communication with a datastorage medium and a processor memory. The data storage medium may beany standard computer data storage device, such as a USB drive, memorystick, hard disk, removable RAM, EPROMs, EAROMs, flash memories andoptical disks or other commonly used memory storage system known to oneof ordinary skill in the art including Internet based storage. The datastorage medium may store one or more programs that when executed causesinformation processor to execute the disclosed method(s). Herein,“information” may include raw data, processed data, analog signals, anddigital signals.

FIG. 2 is a section of drill string 106 in accordance with embodimentsof the present disclosure. The tool section may be located in the BHA108 close to the drill bit (not shown). The tool includes acommunication unit 218 and power supply 220 for two-way communication tothe surface and supplying power to the downhole components. A downholecontroller and processor 117 in accordance with the present disclosurecarry out subsequent control. Stabilizers 208 and 210 for stabilizingthe tool section of the drill string 106 and packers 204 and 206 forsealing a portion of the annulus. A circulation valve disposedpreferably above the upper packer 204 is used to allow continuedcirculation of drilling mud above the packers 204 and 206 while rotationof the drill bit is stopped. A separate vent or equalization valve (notshown) may be used to vent fluid from the test volume between thepackers 204 and 206 to the upper annulus. This venting reduces the testvolume pressure, which is required for a draw down test. It is alsocontemplated that the pressure between the packers 204 and 206 could bereduced by drawing fluid into the system or venting fluid to the lowerannulus, but in any case some method of increasing the volume of theintermediate annulus to decrease the pressure will be required. In oneembodiment of the present disclosure an extendable pad-sealing element202 for engaging the borehole wall (FIG. 2) may be disposed between thepackers 204 and 206 on the test apparatus 216 of the present disclosure.The pad-sealing element 202 could be used without the packers 204 and206, because a sufficient seal with the well wall can be maintained withthe pad 202 alone.

If packers 204 and 206 are not used, a counterforce may be provided sopad 202 can maintain sealing engagement with the wall of the borehole104. The seal creates a test volume at the pad seal. One way to ensurethe seal is maintained is to stabilize the drill string 106. Selectivelyextendable gripper elements 212 and 214 could be incorporated into thedrill string 106 to anchor the drill string 106 during the test.Grippers 212 and 214 are shown incorporated into the stabilizers 208 and210 in this embodiment. Grippers 212 and 214 may protect other elementsfrom damage due to tool movement (e.g, in offshore systems).

FIG. 3 illustrates a formation sampling tool in accordance withembodiments of the present disclosure. Selectively extendable gripperelements 212 engage the borehole wall 105 to anchor the drill string106. Packer elements 204 and 206 extend to engage the borehole wall 105.The extended packers separate the well annulus into three sections, anupper annulus 302, an intermediate annulus 304 and a lower annulus 306.The sealed annular section (or simply sealed section) 304 is adjacent aformation 119. Mounted on the drill string 106 and extendable into thesealed section 204 is the selectively extendable pad sealing element202. A fluid line providing fluid communication between pristineformation fluid 308 and tool sensors such as pressure sensor 324 isshown extending through the pad member 202 to provide a port 320 in thesealed annulus 304. Packers 304 and 306 may be sealingly urged againstthe wall 105 and may have a sealed relationship between the wall 105 andextendable element 202 to ensure pristine fluid is tested or sampled.Reducing pressure in sealed section 304 prior to engaging the pad 202will initiate fluid flow from the formation into the sealed section 304.The port 320 extending through the pad 220 will be exposed to pristinefluid 308.

FIG. 4 illustrates a wireline tool in accordance with embodiments of thepresent disclosure in communication with the formation. Borehole 410intersects a portion of the earth formation 411. Disposed within theborehole 410 by means of a conveyance device 412 is a sampling andmeasuring instrument 413. Conveyance device 412 may be a drill string,coiled tubing, a slickline, an e-line, a wireline, etc. The sampling andmeasuring instrument includes hydraulic power system 414, a fluid samplestorage section 415 and a sampling mechanism section 416. Samplingmechanism section 416 includes selectively extensible well engaging padmember 417, a selectively extensible fluid admitting sampling probemember 418 and bi-directional pumping member 419. Specific configurationof the components with respect to one another may vary.

In operation, sampling and measuring instrument 413 is positioned withinborehole 410 via conveyance device 412 (e.g., by winding or unwindingcable 412 from a hoist (not shown)). Depth information from a depthindicator 421 is coupled to signal processor 422 and recorder 423 wheninstrument 413 is disposed adjacent an earth formation of interest.Control signals from control circuitry 424 are transmitted throughelectrical conductors contained within conveyance device 412 toinstrument 413. Any or all of signal processor 422, control circuitry424 and recorder 423 may be implemented with one more processors.

Electrical control signals activate an operational hydraulic pump withinthe hydraulic power system 414 shown, which provides hydraulic powercausing the well engaging pad member 417 and the fluid admitting member418 to move laterally from instrument 413 into engagement with the earthformation 411 and the bi-directional pumping member 419. Fluid admittingmember or sampling probe 418 can then be placed in fluid communicationwith the earth formation 411, such as, for example, via electricalcontrol signals from control circuits 424 selectively activatingsolenoid valves within instrument 413 for the taking of a sample ofconnate fluids contained in the earth formation of interest, or viaother actuation techniques.

FIG. 5 shows a down hole formation multi-tester instrument in accordancewith embodiments of the present disclosure. Instrument 500 includes abi-directional formation fluid pump which may be included in formationtesting instrument 413. The pump of FIG. 5 is configured to pumpformation fluid into the well bore during pumping to free the sample offiltrate and pump formation fluid into a sample tank after sample cleanup.

Formation testing instrument 413 includes a bi-directional piston pumpmechanism 524. Within the instrument body 413 is also provided one ormore sample tanks, 526 and 528. The piston pump mechanism 524 defines apair of opposed pumping chambers 562 and 564 which are disposed in fluidcommunication with the respective sample tanks via supply conduits 534and 536. Discharge from the respective pump chambers 562, 564 to thesupply conduit of a selected sample tank 526 or 528 is controlled byelectrically energized three-way valves 527 and 529 or by any othersuitable control valve arrangement enabling selective filling of thesample tanks. The respective pumping chambers 562 and 564 are also shownto have the capability of fluid communication with the subsurfaceformation of interest via pump chamber supply passages 538 and 540,which are defined by the sample probe 418 (FIG. 12) and which arecontrolled by appropriate valving. The supply passages 538 and 540 maybe provided with check valves 539 and 541 to permit overpressure of thefluid being pumped from the chambers 562 and 564 if desired. PositionSensor Resistor LMP 47 tracks the position and speed of pistons 558 and560 from which pumping volume, over time, for a known piston cylindersize can be determined, as known in the art.

A point of novelty of the systems and devices illustrated in FIGS. 1-5is that the surface processor and/or the downhole processor (and/orother circuitry) are configured to perform certain methods (discussedbelow) that are not in prior art.

Generally, embodiments of the present disclosure relate to estimation ofan adjustment pressure which may be used as a correction factor whendetermining p(t). Dimensionless adjustment pressure, p_(a,d), may becalculate according to:

$\begin{matrix}{p_{a,d} = {\frac{1}{\sqrt{1 - {4\; c_{d}}}}\left( {{^{\beta_{1}^{2}t_{d}} \cdot {{erfc}\left( {\beta_{1}\sqrt{t_{d}}} \right)}} - {^{\beta_{2}^{2}t_{d}} \cdot {{erfc}\left( {\beta_{2}\sqrt{t_{d}}} \right)}}} \right)}} & (1)\end{matrix}$

which may be calculated using

${\beta_{1} = \frac{1 - \sqrt{1 - {4\; c_{d}}}}{2\; c_{d}}},{\beta_{2} = \frac{1 + \sqrt{1 - {4\; c_{d}}}}{2\; c_{d}}},{c_{d} = \frac{V_{s}c_{s}}{4\; \pi \; r_{s}^{3}\varphi \; c_{t}}},{t_{d} = \frac{tk}{r_{s}^{2}{\mu\varphi}\; c_{t}}},{r_{s} = \frac{G_{o}r_{p}}{4\; \pi}},{and}$c_(t) = c_(r) + S_(o) ⋅ c_(o) + S_(w) ⋅ c_(w) + S_(g) ⋅ c_(g),

wherein:c_(d) is dimensionless tool storage;t_(d) is dimensionless time;t is time;r_(s) is effective probe radius;r_(p) is probe radius;k is predicted formation permeability;φ is formation porosity;μ is formation fluid viscosity;q is constant drawdown rate;G_(o) is geometric factor;V_(s) is system volume;c_(s) is tool system compressibility;c_(t) is total compressibility;c_(r) is rock (formation) compressibility;c_(o) is oil compressibility;c_(w) is water compressibility;c_(g) is gas compressibility;S_(o) is oil saturation;S_(w) is water saturation; andS_(g) is gas saturation.

The term φc_(t) may be treated as a single unknown factor. Theadjustment pressure p_(a) can be calculated from dimensionlessadjustment pressure using Eq. (2).

$\begin{matrix}{p_{a} = {p_{a,d} \cdot \frac{q\; \mu}{G_{o}r_{p}k}}} & (2)\end{matrix}$

Adjustment pressure may be expressed as a function of time, t.Adjustment pressure may be added to initial formation pressure p_(i), orsubtracted from measured pressure p(t). The modified p(t) as used in FRAmay thus be described by Eq. 3.

$\begin{matrix}{{p(t)} = {p_{i} + p_{a} - {\frac{V_{s}c_{s}\mu}{G_{o}r_{p}k}\frac{p}{t}} - \frac{q\; \mu}{G_{o}r_{p}k}}} & (3)\end{matrix}$

FIGS. 6A and 6B show charts of dimensionless adjustment pressure,p_(a,d), with respect to dimensionless time, t_(d). Each curve 602-620represents one of five typical values of dimensionless tool storage.FIG. 6A illustrates a case where the rate is constant. FIG. 6B reflectsa pretest of a draw-down and a build-up. FIG. 6B illustrates a casewhere the rate during build-up is zero. The dimensionless p_(a,d) underthis condition can be obtained by superposition. FIG. 6B shows curves ofdimensionless p_(a,d) with respect to dimensionless t_(d) where build-upstarts at t_(d)=10. An FRA plot according to prior art methods willexhibit a hockey-stick shape when pretest is conducted in a very lowmobility formation (see FIG. 7A). The plot of p_(a,d) as shown in FIG.6B helps to explain this effect. During draw-down and early time ofbuild-up, the adjustment pressure p_(a,d) is greater than zero.Consequently, the pressure measurement p(t) is overvalued by the amountof p_(a). By subtracting p_(a) from the pressure measurement p(t), thehockey-stick shape will be transformed into a straight line.

The correction of estimated parameter values resulting from theembodiments described herein may be illustrated using the followingexample case. Taking an example wherein total test time is 2000 seconds,and the drawdown rate is 1.0 cubic centimeters with a duration of 1.5seconds, the following table provides the relevant system parameters.

TABLE 1 Input Parameters Probe radius r_(p) = 0.635 cm Wellbore radiusr_(w) = 10.795 cm (diameter is 8.5 inch) Porosity φ = 0.2 Permeability k= 0.01 mD Viscosity μ = 1.0 cp Initial formation Pressure p_(i) = 5000psi Total compressibility c_(t) = 9e−6 psi⁻¹ System compressibilityc_(s) = 3e−6 psi⁻¹ System volume V_(s) = 131 cm³

FIG. 7A compares an FRA plot 702 created using the prior art methodagainst an FRA plot 704 determined by correcting p(t) as determinedaccording to the prior art method using an adjustment pressurecorrection factor according to the present disclosure. It is apparentthat the modified FRA plot is a straight line. That overlapping of plots702 and 704 during late build-up portion (from 3500 to 5000 psi)suggests accurate formation mobility can be estimated from late build-upportion of plot 702 using the prior art method. FIG. 7B shows theadjustment pressure 706 for this case with respect to time. The maximumvalue of the adjustment pressure for this case is 1196.9 psi at the endof draw-down (1.5 second). The maximum value of dimensionless adjustmentpressure can be obtained given estimated formation mobility. Then thedimensionless tool storage can be estimated from a chart similar to FIG.6B by matching the maximum value of dimensionless adjustment pressure.

FIG. 8 shows a flow chart 800 for estimating a parameter of interest ofan earth formation intersected by a borehole in accordance withembodiments of the present disclosure. Optional step 810 of the methodcomprises obtaining flow rate analysis information relating to fluidsampling. This may be carried out by sampling fluid from the formationvia a probe contacting a wall of the borehole; taking fluid pressuremeasurements over time; and determining a volume of the sampled fluid asa function of time. The information may be used in determining acorresponding draw rate and/or a corresponding build-up rate of theformation fluid as a function of time.

Optional step 820 may include determining the correction factor. Thecorrection factor compensates for total compressibility. The correctionfactor may be determined using a complementary error function withestimated dimensionless tool storage, or by using estimated formationporosity and estimated formation permeability (or mobility). Determiningthe correction factor may be carried out using a geometric factor. Thegeometric factor G₀ may function to extend application of the methodfrom isotropic formations to anisotropic formations. Superposition mayalso be used, such as, for example, in variable-rate applications.Determining the correction factor may be determined using both draw-downand build-up measurements.

Step 830 comprises using a correction factor to conduct a flow rateanalysis on the fluid sampled from the formation. At step 840, theparameter of interest is estimated. Estimating the parameter of interestmay be carried out by determining a mobility of the formation using aslope of a linear relationship of a time-dependent pressure of the fluidwith respect to a formation flow rate. In some embodiments, theparameter of interest is the mobility. In other embodiments, a parameterof interest such as permeability or viscosity may be determined usingthe mobility.

FIG. 9 shows a flow chart 900 for using a correction factor to conduct aflow rate analysis on the fluid sampled from the formation in accordancewith embodiments of the present disclosure. At step 910, at least one ofi) system compressibility; ii) initial formation pressure; and a productof formation porosity and total compressibility is determined. Step 920comprises applying the correction factor to pressure measurements of thesampled fluid to derive the time-dependent pressure. At step 930, amobility of the formation is determined using a slope of a linearrelationship of a time-dependent pressure of the fluid with respect to aformation flow rate.

The term “conveyance device” as used above means any device, devicecomponent, combination of devices, media and/or member that may be usedto convey, house, support or otherwise facilitate the use of anotherdevice, device component, combination of devices, media and/or member.Exemplary non-limiting conveyance devices include drill strings of thecoiled tube type, of the jointed pipe type and any combination orportion thereof. Other conveyance device examples include casing pipes,wirelines, wire line sondes, slickline sondes, drop shots, downholesubs, BHA's, drill string inserts, modules, internal housings andsubstrate portions thereof, self-propelled tractors. As used above, theterm “sub” refers to any structure that is configured to partiallyenclose, completely enclose, house, or support a device. The term“information” as used above includes any form of information (Analog,digital, EM, printed, etc.). The term “processor” herein includes, butis not limited to, any device that transmits, receives, manipulates,converts, calculates, modulates, transposes, carries, stores orotherwise utilizes information. A processor refers to any circuitryperforming the above, and may include a microprocessor, resident memory,and/or peripherals for executing programmed instructions, applicationspecific integrated circuits (ASICs), field programmable gate arrays(FPGAs), or any other circuitry configured to execute logic to performmethods as described herein. The term very low mobility, as describedherein refers to mobility below 1.0 millidarcy per centipoise, 0.75millidarcy per centipoise, 0.5 millidarcy per centipoise, 0.3 millidarcyper centipoise, 0.1 millidarcy per centipoise, or lower. Fluid, asdescribed herein, may refer to a liquid, a gas, a mixture, and so on.Predicted formation permeability and predicted formation mobility referto values predicted for the formation and used to estimate thecorrection factor. Predicted values may be predicted from lithology,estimated from other estimation techniques, obtained by analogy, and soon, but are distinguished from parameters of interest estimatingaccording to the methods disclosed herein.

While the foregoing disclosure is directed to the one mode embodimentsof the disclosure, various modifications will be apparent to thoseskilled in the art. It is intended that all variations be embraced bythe foregoing disclosure.

What is claimed is:
 1. A method for estimating a parameter of interestof an earth formation intersected by a borehole, the method comprising:using a correction factor to conduct a flow rate analysis on fluidsampled from the formation via a probe contacting a wall of theborehole, wherein the correction factor compensates for totalcompressibility.
 2. The method of claim 1, further comprisingdetermining at least one of: i) the product of formation porosity andtotal compressibility; ii) system compressibility; and iii) initialformation pressure.
 3. The method of claim 1, further comprisingdetermining a mobility of the formation using a slope of a linearrelationship of a time-dependent pressure of the fluid with respect to aformation flow rate.
 4. The method of claim 3, further comprisingapplying the correction factor to pressure measurements of the sampledfluid to derive the time-dependent pressure.
 5. The method of claim 4,further comprising: sampling the fluid from the formation; taking fluidpressure measurements over time; determining a volume of the sampledfluid as a function of time; and determining a corresponding draw rateof the formation fluid as a function of time.
 6. The method of claim 1,wherein the parameter of interest is at least one of: i) formationmobility; and ii) formation permeability.
 7. The method of claim 1,wherein the correction factor is determined using at least one of: i) acomplementary error function; and ii) a numerical inversion of a laplacetransform.
 8. The method of claim 1, wherein the correction factor isdetermined using estimated formation porosity and at least one of: i)predicted formation permeability; and ii) predicted formation mobility.9. The method of claim 1, wherein the correction factor is determinedusing a geometric factor.
 10. The method of claim 1, wherein thecorrection factor is determined using both draw-down and build-upmeasurements.
 11. The method of claim 1, wherein the correction factoris determined using superposition.
 12. The method of claim 1, whereinthe correction factor is determined using formation compressibility. 13.The method of claim 1, wherein the correction factor is determined usingat least one of: i) gas saturation; ii) oil saturation; and iii) watersaturation.
 14. An apparatus for estimating a parameter of interest ofan earth formation intersected by a borehole, the apparatus comprising:a tool body; a fluid sampling unit associated with the tool bodyconfigured to sample fluid from the formation while in the borehole, thefluid sampling unit including a probe configured to contact a wall ofthe borehole; and a processor configured to use a correction factor toconduct a flow rate analysis on fluid sampled from the formation by thefluid sampling unit, wherein the correction factor compensates for totalcompressibility.
 15. The method of claim 14, further comprisingdetermining at least one of: i) the product of formation porosity andtotal compressibility; ii) system compressibility; and iii) initialformation pressure.
 16. The apparatus of claim 14, wherein the processoris configured to determine a mobility of the formation using a slope ofa linear relationship of a time-dependent pressure of the fluid withrespect to a formation flow rate.
 17. The apparatus of claim 16, whereinthe processor is configured to apply the correction factor to pressuremeasurements of the sampled fluid to derive the time-dependent pressure.18. A method for estimating a parameter of interest of an earthformation intersected by a borehole, the method comprising: modeling theformation using an adjusted time-dependent pressure of a fluid sampledfrom the formation through a probe extending to the formation through awall of the borehole, wherein the adjusted time-dependent pressure isdetermined by applying a correction factor compensating for totalcompressibility to time-dependent pressure measurements of the fluid.19. A non-transitory computer-readable medium product havinginstructions thereon that, when executed, cause at least one processorto perform a method, the method comprising: using a correction factor toconduct a flow rate analysis on fluid sampled from the formation via aprobe contacting a wall of the borehole, wherein the correction factorcompensates for total compressibility.
 20. The non-transitorycomputer-readable medium product of claim 19 further comprising at leastone of: (i) a ROM, (ii) an EPROM, (iii) an EEPROM, (iv) a flash memory,or (v) an optical disk.